1. Field of the Invention
The present invention relates to the field of filter adaptation and system identification in the presence of noise.
2. Description of the Related Art
System identification refers to the construction of mathematical models of a dynamic system based upon measured data. One type of mathematical model used to emulate the behavior of physical plants is the linear Autoregressive Moving Average (ARMA) model. In developing such a model, typically parameters of the model are adjusted until the output of the model coincides with that of the actual system output. The accuracy of a model can be evaluated using conventional Mean Squared Error (MSE) techniques to compare the actual system output with the predicted output of the mathematical model.
System identification is an important aspect of designing controllers for physical plants. Accurate system identification facilitates the design of robust controllers. System identification, however, can be imprecise when sensors of the physical plant being modeled collect noise in addition to data.
One conventional method of dealing with noise has been to condition a received signal in the hopes of minimizing or removing noise. Because noise and signal bands overlap in most cases, signal conditioning or filtering, at best, presents a compromise in that the noise cannot be removed from the signal bands.
Moreover, conventional MSE-based techniques are not useful indicators of model accuracy when data has been corrupted with additive white noise or noise which is similar to, or can be modeled as white noise. It has been widely acknowledged that MSE is optimal for linear filter estimation when there are no noisy perturbations on the data. For many real-world applications, however, the “noise-free” assumption is easily violated and using MSE-based methods for parameter estimation can result in severe parameter bias.
What is needed is a technique for estimating model parameters for a physical plant which provides acceptable results in the presence of noise.